A train is accelerating at a rate of 2 m/s. If it's initial velocity is 20 m/s, what is its velocity after 30 seconds?

We don't know anything about the direction of the track, so we can't say anything about the train's 'velocity'. The best we can do is talk about its speed.

Speed = (initial speed) + (acceleration) x (time spent accelerating)

Speed = (20 m/s) + (2 m/s²) · (30 sec)

Speed = (20 m/s) + (60 m/s)

Speed = 80 m/s

(This is about 179 miles per hour, so if this is not a bullet train of some kind, then get ready for an ugly crash.)

The formula for acceleration is ::

Acceleration = (Final Velocity - Initial Velocity) / Time

Therefore, to work out the final velocity, we must isolate the variable in the formula. This is done by multiplying both sides by Time, and adding both sides by Initial Velocity; leaving the final velocity on its own as follows::

(Acceleration/Time) + Initial Velocity = Final Velocity

If we now substitute our values into the equation, we get 2*30 + 20 = 80

80m/s is the final velocity!